On 2-path signed graphs

Abstract

A signed graph (sigraph) is a graph where each edge receives positive or negative sign. In this paper, we report our investigation on a new signed graph (S) ₂ called 2-path sigraphs of a given sigraph S defined as that sigraph whose vertex set is the vertex set of S and two vertices in (S) ₂ are adjacent if there exist a path of length two between them in S and negatively signed if all the paths of length two between them are all-negative, otherwise positively signed.